Query to check whether user has datapump privilege.

Check for whether user has full database export/import privilege
You can check whether user has privilege to export or import the full database using data pump. To export full database using data pump user must have EXP_FULL_DATABASE role or dba role and to import full database using data pump user must have IMP_FULL_DATABASE or dba role.
In order to see whether user has these privilege or not you can query,

SQL>SET lines 100
COL privilege FOR a50
SELECT grantee, granted_role, default_role
FROM dba_role_privs
WHERE granted_role IN ('DBA', 'EXP_FULL_DATABASE', 'IMP_FULL_DATABASE')
ORDER BY 1,2; 
GRANTEE                        GRANTED_ROLE                   DEF
------------------------------ ------------------------------ ---
SHAIK                          DBA                            YES
DBA                            EXP_FULL_DATABASE              YES
DBA                            IMP_FULL_DATABASE              YES
FARUK                          DBA                            YES
MOMIN                          DBA                            YES
SYS                            DBA                            YES
SYS                            EXP_FULL_DATABASE              YES
SYS                            IMP_FULL_DATABASE              YES
SYSMAN                         DBA                            YES
SYSTEM                         DBA                            YES
TEST                           EXP_FULL_DATABASE              YES

which indicates user SHAIK,FARUK,MOMIN,SYS,SYSTEM can do both full data pump export and full datapump import operation. And user Test only has datapump export operation. Note that DBA role includes both EXP_FULL_DATABASE and IMP_FULL_DATABASE roles.

Check for user has create table or create session privilege
In order to see whether a user has CREATE TABLE or CREATE SESSION privilege, query from dba_sys_privs table. Following is the check whether user TEST has these privilege or not.

SQL>SET lines 100 pages 100
COL privilege FOR a40
SELECT grantee, privilege
 FROM dba_sys_privs
WHERE (grantee IN ('TEST', 'PUBLIC')
       OR grantee IN (SELECT granted_role FROM dba_role_privs
                       WHERE grantee IN ('TEST', 'PUBLIC')))
  AND privilege IN ('CREATE SESSION', 'CREATE TABLE')
ORDER BY 1,2;   
If user test have it then output will be like below.
GRANTEE                        PRIVILEGE
------------------------------ ----------------------------------------
TEST                           CREATE SESSION
TEST                           CREATE TABLE

Check for granted privileges on directory objects
Suppose we want to check whether user TEST has privilege on directory objects query,

SET lines 110
COL privilege FOR a12
COL grantee FOR a25
COL owner FOR a25
SELECT p.grantee, p.privilege, p.owner, d.directory_name
 FROM dba_tab_privs p, dba_directories d
WHERE p.table_name=d.directory_name
  AND (grantee IN ('TEST', 'PUBLIC')
       OR grantee IN (SELECT granted_role FROM dba_role_privs
                       WHERE grantee IN ('TEST', 'PUBLIC')))
ORDER BY 4,3,2;
A typical output is
GRANTEE              PRIVILEGE  OWNER                DIRECTORY_NAME
-------------------- ---------- -------------------- ------------------------------
TEST                 READ       SYS                  D
TEST                 WRITE      SYS                  D
EXP_FULL_DATABASE    READ       SYS                  DATA_PUMP_DIR
EXP_FULL_DATABASE    WRITE      SYS                  DATA_PUMP_DIR

Check for default tablespace on a user
In order to check what is the default tablespace of user TEST query,

SQL>select default_tablespace from dba_users where username='TEST';

Check for tablespace quota
To check whether user TEST has quota on which tablespaces query,
SET lines 100 numwidth 12
SELECT q.username, q.tablespace_name, q.bytes, q.max_bytes
 FROM dba_ts_quotas q, dba_users u
WHERE q.username=u.username AND q.username in ('TEST'); 
USERNAME                       TABLESPACE_NAME                       BYTES    MAX_BYTES
------------------------------ ------------------------------ ------------ ------------
TEST                           SYSTEM                                65536     10485760

From output we can see user TEST has quota on system tablespace 10M and he already used 65K.